Methods for making high strength ceramic elements

ABSTRACT

One embodiment of the present invention relates to spherical ceramic elements, such as proppants, for maintaining permeability in subterranean formations to facilitate extraction of oil and gas therefrom. The strength of the ceramic element may be enhanced by combining materials having different coefficients of thermal expansion. Methods of making the ceramic elements are also disclosed.

This application claims the benefit of U.S. Provisional Application No.60/906,464, filed Mar. 12, 2007, and incorporated by reference.

BACKGROUND OF THE INVENTION

This invention generally relates to ceramic elements for use in a widevariety of industrial applications. Some of these applications includeusing the ceramic elements: as a proppant to facilitate the removal ofliquids and/or gases from geological formations; as a media forscouring, grinding or polishing; as a bed support media in a chemicalreactor; as a heat transfer media; and as a filtration media. Morespecifically, this invention is useful in applications that require aceramic sphere that has high crush resistance. Even more specifically,this invention pertains to proppants that may be used in geologicalformations where the pressure exerted on the proppant exceeds the crushresistance of conventional proppants such as sand and resin coated sand.

Examples of patents and published patent applications directed toproppants include: U.S. Pat. No. 4,632,876; U.S. Pat. No. 7,067,445; andUS 2006/0177661.

BRIEF SUMMARY OF THE INVENTION

In one embodiment, this invention may be a spherically shaped ceramicelement comprising a sintered base secured to a sintered layer. The basehas a coefficient of thermal expansion and the layer has a coefficientof thermal expansion. The base's coefficient of thermal expansionexceeds the layer's coefficient of thermal expansion. The base exerts acompressive force on the layer.

In another embodiment, this invention may be a process for manufacturinga ceramic element. The process may include the following steps. Forminga spherically shaped non-sintered base of sinterable ceramic material.Depositing a non-sintered layer of sinterable material on the surface ofthe base thereby forming a spherically shaped non-sintered compositehaving a base coated with at least one layer. Exerting a compressiveforce on the ceramic element by exposing the composite to a completethermal cycle that includes a thermal ramp up phase and a thermal cooldown phase. During the ramp up phase the base bonds and shrinks morethan the layer. After the cool down phase the base exerts a compressiveforce on the layer.

In another embodiment, this invention may be a process for manufacturinga ceramic element. The process may include the following steps. Forminga spherically shaped non-sintered base of sinterable ceramic material.Depositing a non-sintered layer of sinterable material on the surface ofthe base thereby forming a spherically shaped non-sintered compositehaving a base coated with at least one layer. Exposing the composite toa complete thermal cycle comprising at least a first thermal ramp upphase and a final thermal cool down phase. After the initiation of thefirst ramp up phase the base shrinks and the layer applies a compressiveforce to the base. After the initiation of the final cool down phase atleast a portion of the layer separates from the base.

In yet another embodiment, this invention may be another process formanufacturing a ceramic element. The process may include the followingsteps. Forming a spherically shaped non-sintered base of sinterableceramic material. Heating the base to achieve at least partial sinteringof the base. Depositing a non-sintered layer of sinterable material onthe surface of the base thereby forming a spherically shaped compositehaving at least a partially sintered base coated with a non-sinteredlayer. Exposing the composite to a complete thermal cycle that exceedsthe sintering temperatures of the base and layer. During the thermalcycle the base and layer bond to one another and contraction of the baseexerts a compressive force on the layer.

The present invention may relate to a method of propping a geologicalformation. The method may include the steps of mixing a plurality ofproppants with a fluid to form a flowable mixture and forcing themixture under pressure into the geological formation until at least aportion of the proppants are disposed into cracks in the formation,wherein at least 5 weight percent of the proppants each comprises asintered base secured to a sintered layer and the base exerts acompressive force on the layer.

The present invention may relate to another method of propping ageological formation. This method may include the steps of mixing aplurality of proppants with a liquid to form a flowable mixture. Theproppant comprises a sintered base bonded to a sintered layer and thebase exerts an initial force on the layer. Disposing the mixture underpressure into the geological formation until at least a portion of theplurality of proppants is inserted into fissures in the formation.Utilizing geothermal heat supplied by the geological formation to heatthe proppants wherein the heat causes the exertion of a net compressiveforce on the layer and the net compressive force exceeds the initialforce.

“Sintering”, as used herein, means the joining of particles through theapplication of heat. This commonly results in densification, but not inall cases.

“Crush resistance” of a proppant is a term commonly used to denote thestrength of a proppant and may be determined using ISO 13503-2:2006(E).A strong proppant generates a lower weight percent crush resistance thana weak proppant. For example, a proppant that has a 2 weight percentcrush resistance is considered to be a strong proppant and is preferredto a weak proppant that has a 10 weight percent crush resistance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a hypothetical plot of percent linear change versus timefor a homogenous material;

FIG. 2 shows hypothetical plots of percent linear change versus time fortwo materials;

FIG. 3 is a photograph, magnified approximately 100 times, of aconventional proppant for comparison to a proppant of this invention;

FIG. 4 is a photograph, magnified approximately 150 times, of a firstembodiment of a proppant of this invention;

FIG. 5 is a photograph, magnified approximately 120 times, of a secondembodiment of a proppant of this invention;

FIG. 6 shows the steps of a first process for manufacturing a proppantof this invention;

FIG. 7 shows the steps of a second process for manufacturing a proppantof this invention;

FIG. 8 shows the steps of a third process for manufacturing a proppantof this invention;

FIG. 9 shows the process steps for fracturing a subterranean formation;and

FIG. 10 is a photograph, magnified approximately 180 times, of aproppant for comparison to a proppant of this invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a proppant with crush resistance that canbe tailored for use in shallow wells, which are less than 500 m deep,intermediate wells, which may be between 500 m and 1500 m deep, or deepwells which are in excess of 1500 m below the surface of the ground. Theproppant may be made from a combination of ceramic materials which canbe selected to achieve maximum crush resistance.

The invention relates to proppants that are useful in increasing theoutput of oil and gas wells which may be located in porous and permeablesubterranean formations. The porosity of the formation permits theformation to store oil and gas, and the permeability of the formationpermits the oil or gas fluid to move through the formation. Sometimesthe permeability of the formation holding the gas or oil is insufficientfor economic recovery of oil and gas. In other cases, during operationof the well, the permeability of the formation drops to such an extentthat further recovery becomes uneconomical. In such circumstances, it iscommon to fracture the formation, thereby creating cracks within theformation, and then force a suitable quantity of proppant into thecracks thereby holding them open so that the gases and liquids thatwould otherwise be trapped can readily flow through the cracks. Suchfracturing is usually accomplished by using a hydraulic pump to force agel-like fluid down a bore hole. The pressure is increased until cracksform in the underground rock. The proppants, which are suspended in thispressurized fluid, are forced into the cracks or fissures. When thehydraulic pressure is reduced, at least a portion of the proppantmaterial remains in the cracks and functions to prevent the formedfractures from closing.

Depending on the geological conditions, a wide variety of proppantmaterials may be used. Typically, proppants are particulate materials,such as sand, glass beads, or ceramic pellets, which create a porousstructure. Shown in FIG. 3 is a photograph of a cross-sectional view ofa conventional ceramic proppant 10 which is a generally sphericalparticle. The interstices between the particles allow the oil or gas toflow to collection regions. Pumps are used to move the oil or gas to thewell head. Over time, the pressure of the surrounding rock tends tocrush the proppants. The resulting fines from this disintegration tendto migrate and plug the interstitial flow passages in the proppedstructure. These migratory fines may drastically reduce the conductivityof the proppant which is a measure of the ease with which oil or gas canflow through the proppant structure and may be important to theproductivity of a well. When the proppant's conductivity drops below acertain level, the fracturing process may be repeated or the well may beabandoned.

Ceramic proppants, sometimes called man-made proppants, are favored incertain applications over natural proppants, such as sand orresin-coated sand, due to the ceramic proppant's ability to withstandhigh pressures and temperatures and their resistance to corrosion.Despite being made of higher cost materials than natural materials, theimproved crush resistance of ceramic renders the ceramic proppantssuitable for conditions which are too severe for other materials, e.g.,at rock pressures above about 350 kg/cm² (5,000 psi). As pressureincreases with depth, ceramic proppants are commonly used at depths ofabout 1500 meters below the earth's surface, or more. They are typicallyformed by combining finely ground material, such as clay, bauxite, orcorundum, with water and then mixing in a rotary mixer. Blades in themixer cause the wet mixture to form generally spherical pellets, whichupon drying and sintering at high temperature are of the generalparticle size desired. Pellets which fall outside the desired range arereturned to the mixer after the drying stage to be reworked.

Proppants may be generally classified into one of three grades: lightweight proppants (LWP), intermediate grade proppants (IP), and highstrength proppants (HSP). Light weight proppants are suitable for useover a range of closure stress from less than about 1000 psi to about7500 psi, while intermediate grade proppants are useful up to about12,000 psi, and high strength proppants can be used at pressures inexcess of 12,000 psi. Attempts to improve conductivity have focused onmethods of improving crush resistance of the proppants. One methodincludes the application of coatings. While measurable improvements inconductivity have been obtained, for example, by applying a resincoating, such improvements have associated increases in cost.

The present invention achieves the goal of producing a proppant havingdesirable crush resistance by selecting material combinations andprocessing steps that result in the exertion of a net compressive forceon the proppant's layer by the proppant's base. Providing a proppanthaving desirable crush resistance due to the creation of a netcompressive force on the layer by the base requires significantknowledge, skill and a previously unidentified appreciation of howmaterial selection and proppant design may be coordinated to produce aproppant having certain desired characteristics. In addition to crushresistance, properties such as permeability, chemical compatibility,particle size distribution, availability of raw materials and processinglimitations may be considered when specifying a proppant. From the widearray of options available to proppant manufacturers, the inventors haveidentified and described below the material properties, proppant designcriteria and processing steps that may be brought together to produce aproppant of this invention.

In one embodiment of a ceramic element of the present invention, such asa proppant, sinterable materials having different coefficients ofthermal expansion may be used to create a proppant having a base thatexerts a compressive force on the proppant's layer. The compressiveforce exerted on the layer by the base increases the crush resistance ofthe proppant. As will be explained, the compressive force exerted on theproppant can be produced using a kiln to expose the unfired base andlayer to at least one complete thermal cycle, or, alternatively, theheat transferred to the proppant may be provided by the geologicalformation when the proppant is disposed downhole into a well. As usedherein, “a complete thermal cycle” includes an initial temperature, atleast an initial ramp up phase, at least a final cool down phase and afinal temperature that is equal to or less than the initial temperature.A complete thermal cycle may also include: a thermal holding phasebetween the initial thermal ramp up phase and the final cool down phaseduring which the temperature of the proppant is not intentionallyincreased or decreased; one or more additional ramp up phases; and oneor more additional cool down phases. Factors that can impact theformation of a proppant of this invention may include: the chemistry ofthe proppant's raw materials; the microscopic phase or phases that existwithin the proppant after sintering, the physical relationship of thebase to the layer; and the process steps used to make the proppant.

In a first embodiment of a process for making a proppant of thisinvention, a plurality of spheroids of sinterable material having aknown coefficient of thermal expansion are produced. These spheroids,which may be individually identified herein as an “inner base” or “base”and collectively referred to as “bases”, are similar to commerciallyavailable proppants. A layer of sinterable material, which may bephysically and/or chemically and/or crystallographically distinct fromthe base material, may be disposed on the surface of the spheroid shapedbase thereby forming a nonsintered layer of sinterable material on thesurface of the non-sintered base material which may be collectivelyreferred to herein as a proppant precursor. The layer has a coefficientof thermal expansion less than the base material's coefficient ofthermal expansion. The precursor may then be heated above the minimumtemperature needed to bond the base to the layer and sinter both thebase and the layer. As the bonded and sintered composite cools down, thebase responds to the reduction in temperature by attempting to shrinkmore than the layer shrinks which results in the base exerting acompressive force on the layer. The compressive force improves theproppant's crush resistance.

The improvement in the crush resistance of the proppant may beinfluenced by several variables that include product characteristicsand/or processing steps and combinations of the same. For example, thedifference between the base material's coefficient of thermal expansionand the layer material's coefficient of thermal expansion may be used tocause stresses in ceramic components. Selecting combinations ofmaterials that have complimentary coefficients of thermal expansion andthen processing them in a manner that imparts a desirable compressiveforce on the layer material requires skill and knowledge. Anotherproduct characteristic is the shrinkage of the base material and thelayer material due to densification during the sintering process. Whiledensification of ceramic materials due to sintering is well known, howto select combinations of a base material and a layer material thatresults in the exertion and maintenance of a compressive force on thesintered proppant's layer by the base is not fully appreciated in theart. With regard to processing steps and, in particular, during thesintering process, the difference between the temperatures at which thebase material and layer material begin to shrink (start of shrinkage)and stop shrinking (termination of shrinkage) may favorably influence ornegatively impact the generation of the desired compressive force on thelayer by the base. Furthermore, during the latter portion of thesintering process, the difference in the base material's and the layermaterial's rates of linear change versus temperature can be used toexert a compressive force on the layer. When a proppant precursor issintered, both the sinterable base and sinterable layer may bedensified. The sintering process can reduce the porosity of the materialwhich may reduce the volume occupied by the material. Non-reversiblesintering causes non-reversible shrinkage of the material. In contrast,the repeated expansion and contraction of a material in response toincreases and subsequent decreases in the temperature of the materialmay be a repeatable, reversible and material specific phenomenon thatdefines the material's coefficient of thermal expansion. The shrinkageof a ceramic material due to densification and the shrinkage of the samematerial due to the coefficient of thermal expansion can be treated asindependent from one another and may be coordinated to achieve thedesired compressive force on the layer.

As will now be explained, the relationship between the sinteringprofiles of the base material and layer material may be one of thecharacteristics used to select material combinations that will generatea compressive force on the layer. Shown in FIG. 1 is an exemplary graphwhere the percent of linear change (PLC) is plotted versus temperaturefor a hypothetical material that could be used to form a proppant. Whilethis graph illustrates a single step sintering curve, multiple stepsintering curves, such as a two step curve or a three step curve, arepossible. The percent of linear change may be determined usingdilatometry. A commercially available dilatometer is an Anter model1161. Sintering profile 20 includes a first region 22 where the lengthof the material remains essentially unchanged as the temperature of thematerial is increased. The second region 24 of the sintering profile isdefined by a first temperature 26 at which the material starts to shrinkand a second temperature 28 at which the shrinkage terminates. The thirdregion 30 of the sintering profile begins at temperature 28 andrepresents the region where material no longer shrinks despite furtherincreases in the material's temperature. Temperature 26 indicates thestart of shrinkage and temperature 28 indicates the termination ofshrinkage. Temperature 32 represents the material's nominal sinteringtemperature which may be determined by identifying the point on thecurve where the material has achieved 50% of the amount of shrinkagedisclosed by the curve and then determining the temperature at which the50% shrinkage was achieved. The total amount of shrinkage 34 isrepresented by the difference between the value of the starting lineardimension 36 and the value of the final linear dimension 38.

Shown in FIG. 2 is an exemplary graph of two sintering profiles from ahypothetical base material 40 and a hypothetical layer material 42. Inthis example, when the proppant has reached the final stage ofsintering, which is defined for use herein as the region betweentemperature T₁ and T₂ as shown in FIG. 2, the rate of linear change inthe layer material is less than the rate of linear change in the basematerial. Consequently, as the temperature of the proppant is increasedfrom T₁ to T₂ the base shrinks more than the layer. If the base isadequately bonded to the layer, then the base effectively tries to pullthe layer inwardly toward the center of the proppant thereby exerting acompressive force on the layer. The cross-hatching in FIG. 2 representsthe difference in the rates of linear contraction versus temperature. Ifthis difference in the rates of linear contraction is too small, thenthere will be no compressive force exerted on the layer. If thedifference in the rates of linear contraction is too large, the base maypull away from the layer thereby effectively delaminating the layer fromthe base. Furthermore, if the difference in nominal sinteringtemperature is too small, such as less than 5° C., or too large, such asgreater than 250° C., then the base may not be able to exert acompressive force on the layer. Depending upon the composition of thebase material and layer material a difference in nominal sinteringtemperatures between 20° C. and 150° C. may be desirable.

The absolute difference between the coefficients of thermal expansionmay be between 1% and 40% of the base's coefficient of thermalexpansion. In some embodiments, the absolute difference between thecoefficients of thermal expansion may be between 5% and 30% of thebase's coefficient of thermal expansion. Proppants that experiencedelamination of the layer may have reduced strength and theireffectiveness as a proppant may be diminished.

To illustrate some embodiments of the invention described herein,various combinations of sinterable base material and sinterable layermaterial will now be described. In a first scenario, if the shrinkage ofthe base due to sintering is greater than the shrinkage of the layer dueto sintering and the base is bonded to the layer, then the base mayexert a compressive force on the layer. If, at the same time, the basematerial's coefficient of thermal expansion is greater than the layermaterial's coefficient of thermal expansion, then the difference incoefficients of thermal expansion further increases the compressiveforce exerted on the layer. In a second scenario, if the shrinkage dueto sintering of the base and layer are essentially equal and the basematerial's coefficient of thermal expansion is greater than the layer'scoefficient of thermal expansion, then the compressive force exerted onthe layer may be due solely to the difference in coefficients of thermalexpansion. In a third scenario, if the coefficients of thermal expansionof the base and layer are essentially the same and the shrinkage of thebase due to sintering is greater than the shrinkage of the layer due tosintering, then the compressive force exerted on the layer may be duesolely to the difference in shrinkage caused by the sintering. In afourth scenario, the layer's coefficient of thermal expansion is greaterthan the base's coefficient of thermal expansion and the shrinkage ofthe layer caused by sintering may be greater than the shrinkage of thebase caused by sintering. A proppant having these physicalcharacteristics may or may not experience a net compressive force whenfunctioning as a proppant in a downhole application. For example, aproppant having the characteristics described above in the fourthscenario may experience a compressive force on the layer when thetemperature of the proppant is elevated, such as when the proppant isdisposed into a geological formation where a source of geothermal heatcan increase the temperature of the proppant. In a fifth embodiment, theshrinkage of the base due to sintering is less than the shrinkage of thelayer due to sintering and the base material's coefficient of thermalexpansion is greater than the layer's coefficient of thermal expansion.In a sixth embodiment, the shrinkage of the base due to sintering isgreater than the shrinkage of the layer due to sintering and the layermaterial's coefficient of thermal expansion is greater than the basematerial's coefficient of thermal expansion. In the fifth and sixthembodiments, the specific characteristics of the proppant and theprocessing conditions used to make the proppant may be coordinated toexert a net compressive force on the layer.

Some of the proppant's characteristics that may be used to influence theexistence and/or amount of compressive force exerted on the layer arethe diameter of the base and the thickness of the layer. In turn, thediameter of the base and the thickness of the layer may be impacted bythe raw materials used to make the base and layer. If the difference inthe coefficients of thermal expansion is large, the diameter of the basemay be minimized and the thickness of the layer may be maximized so thatthe shrinkage of the base does not cause the layer to crack and buckleinwardly thereby reducing the proppant's crush resistance. However, ifthe difference in the coefficients of thermal expansion is small, thediameter of the base may be maximized and the thickness of the layerminimized so that the shrinkage of the base can exert sufficientcompression of the layer to adequately improve the proppant's crushresistance. The average thickness of the layer may be between 5% and 50%of the proppant's average radius. Layer thickness between 10% and 25% ofthe proppant's average radius may be desirable.

The physical characteristics of the base and layer may also influencethe creation of a net compressive force on the layer. For example, ifthe base includes particles having an average particle size that exceedsthe average particle size of the layer's particles, the difference inaverage particle size may increase the net compressive force on thelayer by the base.

Determining the existence of a compressive force on a proppant's layermay be determined directly or indirectly. The indirect method requiresthe determination of the base material's coefficient of thermalexpansion and the layer's coefficient of thermal expansion prior tomaking the proppant. The coefficients of thermal expansion may bedetermined using an analytical technique known as dilatometry to plotchanges in both the base material's and the layer material's lengthversus changes in temperature. The changes in length versus temperatureof the raw materials determine the materials' coefficients of thermalexpansion. If the layer's coefficient of thermal expansion is less thanthe inner base's coefficient of thermal expansion, then the base mayexert a compressive force on the layer In comparison to the indirectmethod, the direct method uses diffraction patterns generated by X-raydiffraction (XRD) or transmission electron microscopy (TEM) to determinewhether or not the layer is in compression. This determination isaccomplished by measuring the atomic spacings of certain atoms in thelayer and then comparing these atomic spacings, also known as“d-spacings”, to the atomic spacings of control materials that are notin compression. If the d-spacings of the atoms in the layer are at leastone percent less than the comparable d-spacings in the control material,then the layer may be in compression. The amount of compression may beproportional to the difference in d-spacings between the proppant andthe control material.

Referring now to the drawings and more particularly to FIG. 3, there isshown a magnified photograph of a cross-sectional view of a conventionalceramic proppant 10 which may be a generally spherical particle. Theproppant includes a mixture of sinterable compounds that have been mixedwith one another, formed into spheroids and then sintered in a completethermal cycle thereby forming a plurality of free flowing particles.Suitable sinterable compounds include alumina, titania, silica,magnesia, mullite, talc, forsterite, iron oxide, clay, bauxite andaluminosilicates

Referring now to FIG. 4, there is shown a magnified photograph of across-sectional view of a first embodiment 12 of a ceramic proppant ofthis invention. Proppant 12 comprises base 14 onto which layer 16 hasbeen deposited and bonded. The base may be referred to herein as thecore of the proppant. The layer, which may be described herein as ashell, forms a hard protective coating on the surface of the base due tothe compressive force exerted on the layer by the base. While acontinuous layer that encapsulates base 14 may provide the proppant withthe best crush resistance, a discontinuous layer may be feasible. Adiscontinuous layer may have one or more openings therethrough. Thesize, shape, and location of the openings may not cause a significantreduction in the proppant's crush resistance relative to a proppanthaving a continuous layer.

Shown in FIG. 5 is a magnified photograph of a cross-sectional view of asecond embodiment 18 of a ceramic proppant of this invention. Similar tothe proppant shown in FIG. 4, the proppant shown in FIG. 5 has a base 14and an layer 16. However, in contrast to the proppant shown in FIG. 4,the proppant shown in FIG. 5 has intermediate layer 19 between the baseand layer. The intermediate layer may function as a bonding layerbetween the base and layer. The use of a bonding layer may be usefulwhen the base and layer cannot be readily bonded to one another.

FIG. 6 discloses the steps in a first embodiment of a process for makingceramic proppant of this invention. In step 100, a plurality ofnon-sintered bases, made of sinterable ceramic material, may be formed.In step 102, a non-sintered layer of sinterable material may bedeposited on the surface of the base thereby forming a proppantprecursor. Step 104 represents heating the precursor in a single thermalcycle to at least the minimum temperature needed to bond and sinter thebase and layer and then cooling the bonded base whereby the base exertsa compressive force on the layer.

FIG. 7 discloses the steps in a second embodiment of a process formaking ceramic proppant of this invention. In step 110, a plurality ofnon-sintered bases, made of sinterable ceramic material, may be formed.Step 112 represents sintering and then cooling the bases in a firstthermal cycle. The bases have a maximum theoretical density that may becalculated. The bases may be densified as needed to achieve the physicalintegrity needed. Densification of the bases to at least 25% and lessthan 75% of the base material's maximum theoretical density is feasible.Step 114 represents depositing a layer of non-sintered material on thesintered bases. Step 116 represents sintering of the non-sintered layerin a second thermal cycle. The sintering temperature in step 116 may beat least 25° C. greater than the sintering temperature in step 112.

FIG. 8 discloses the steps in a third embodiment of a process for makingceramic proppant of this invention. In step 140, a plurality ofnon-sintered bases, made of sinterable ceramic material, may be formed.In step 142, a non-sintered layer of sinterable material may bedeposited on the surface of the base thereby forming a composite havinga base coated with at least one layer. Step 144 represents exposing thecomposite to a complete thermal cycle that includes a first thermal rampup phase and a final thermal cool down phase. After initiation of thefirst ramp up phase the base shrinks and the layer applies a compressiveforce to the base. After the initiation of the cool down phase and priorto the separation of the layer from the base, the layer may temporarilyexert an additional compressive force on the base. Ultimately, after theinitiation of the final cool down phase at least a portion of the layerseparates from the base which potentially exposes the base to directcontact with an adjacent proppant.

The process disclosed in FIG. 8 generates a crush resistant proppant byutilizing the layer to exert a compressive force on the base after theinitiation of the first thermal ramp up phase and then relying uponstress imparted to the layer during the thermal cycle to fracture thelayer which leads to the removal of at least a portion of the layer. Theapplication of a compressive force on the base by the layer may becaused by sintering of the layer and/or by the difference between thebase's and layer's coefficients of thermal expansion. Applying acompressive force to the base is believed to improve the strength andthus the crush resistance of the base. Regardless of the reasons for theshrinkage of the layer, if the layer applies a compressive force to thebase then the layer may be in tension. The separation of the layer fromthe base may be caused by the layer having a higher coefficient ofthermal expansion than the base. Separation of the layer from the basemay occur during or after the cool down phase. If at least a portion ofthe layer spontaneously fractures after the initiation of the cool downphase, the fractured portion may readily fall away from base. Additionalportions of the layer may separate from the base if a plurality ofproppants are tumbled or exposed to ultrasonic vibration. The amount oflayer that separates from the base may be proportional to the amount ofstress applied to the layer which may be proportional to the differencein the base's and layer's coefficients of thermal expansion. While thedifference in coefficients of thermal expansion needed to separate thelayer from the base may vary with thickness of the layer, diameter ofthe base, etc, in some embodiments the difference between the base'scoefficient of thermal expansion and the layer's coefficient of thermalexpansion may be at least 40% but not more than 80% of the base'scoefficient of thermal expansion. If the difference in the coefficientsof thermal expansion is too small, the layer may not separate from thebase.

As used herein, the “amount of layer that separates from the base” iscalculated as a percentage of the proppant's surface area. Thiscalculation may utilize an optical or electron microscopy technique todetermine the amount of the proppant's surface area not covered by thelayer. The layer may be described as separating from the proppant if thebase can be seen using an optical technique. In one scenario,essentially all (e.g. 100%) of the layer is removed from the base. Inother embodiments, the amount of layer removed may be no more than 25%,50% or 75% of the proppant's surface area. The layer material thatseparates from the base should be removed from the proppant prior tousing a plurality of proppant in a downhole application.

In contrast to using the processes described above to form a highstrength proppant prior to inserting the proppant into a geologicalformation, the crush resistance of the proppant may be increased afterinsertion of the proppant in the fissures by utilizing the geologicalformation's geothermal heat to increase the temperature of the proppantsafter they have been mixed with a liquid and inserted into the fissures.In some embodiments, this process may utilize differences in thecoefficients of thermal expansion of the proppant's base and layer tocreate a net compressive force. When proppants are inserted intogeological formations, the ambient temperature within the formation mayexceed 50° C. and commonly exceeds 75° C. Proppants that have an layerwith a coefficient of thermal expansion greater than the base'scoefficient of thermal expansion attain a net compressive force as thelayer responds to the increase in temperature by trying to pull awayform the base which has a lower coefficient of thermal expansion andtherefore expands less than the layer. Because the base and layer arebonded to one another, the base restrains the movement of the layerthereby exerting a compressive force on the layer.

The steps of forming a high strength proppant after insertion into thefissures of a formation are disclosed in FIG. 9. Step 120 representsmixing a quantity of proppant having a sintered base and a sinteredlayer disposed on the sintered base with a liquid thereby forming amixture. The base exerts an initial force on the layer. Step 122represents forcing the mixture under pressure into the fissures in theformation. Step 124 represents utilizing the formation's geothermal heatto increase the temperature of the proppants which causes the exertionof a net compressive force on the layer. The net compressive forceexceeds the initial force. The advantages of using a quantity ofproppants as described herein may be best realized if 100 weight percentof the proppants have the features claimed below. However, someadvantage may be realized if only 5 weight percent of the population ofproppants has the desired features. In one embodiment, at least 50weight percent of the population of proppants may have the desiredfeatures. In a second embodiment, at least 90 weight percent of thepopulation of proppants may have the desired features.

Examples Lots A, B, C, and D

To demonstrate the impact of particle size on the crush resistance ofthe invention described above, four lots of proppants, identified belowas lots A, B, C, and D, were manufactured and evaluated for resistanceto crushing. The lots were made by providing a quantity of commerciallyavailable bauxite that was ground to a mean particle size ofapproximately 6 microns and is identified herein as “coarse” material. Aportion of the coarse material was then ground to a mean particle sizebelow 2 microns and is identified herein as “fine” material. Table 1shows the compositions of the base and layer for each of the four lots.

TABLE 1 Base Material Coarse Fine Layer Coarse Lot A Lot B Material FineLot C Lot D

Each lot of proppants was made by forming a spherically shaped base thatwas then coated with a layer thereby forming a composite. The bases weremade using a “wet forming” method that will now be described. First, aquantity of the base material and a drilling starch binder were disposedinto an Eirich mixer and dry mixed for 30 seconds. Water was then addedover a 30 second period as the mixer continued to rotate and spheres ofbase material were formed. After approximately four minutes of mixingthe base material, binder and water, the layer material was slowly addedto the mass of rotating spherically shaped bases by sprinkling (alsoknown as “dusting in”) the layer material on top of the bases as theywere moving in the mixer. All lots were then sintered at 1425° C. Afterforming and sintering all lots had a standard 20/40 size distribution.The strength of each lot was then evaluated using a CAMSIZER by Horibato determine the percent crush at 700 kg/cm². As used herein, the term“percent crush” refers to the weight percent of the crushed quantity ofproppant that flowed through a 40 mesh screen. Shown in Table 2 are theresults of the crush testing.

TABLE 2 Base Material Coarse Fine Layer Coarse Lot A Lot B Material 4.3%12.6% Fine Lot C Lot D 2.6%  4.2%

The data clearly demonstrates that the lowest weight percent crush wasprovided by lot C which was made from a coarse base material and a finelayer material. The reason lot C had the best resistance to crushing, asevidenced by the lowest weight percent crush, is believed to be due tothe difference in shrinkage rates between the base material and thelayer material. During the final stage of sintering, the coarse basematerial shrunk at a faster rate than the layer material. Since the baseand layer are inherently bonded to one another during the sinteringprocess, the difference in the rate of linear contraction during thefinal stage of sintering resulted in the base exerting a compressiveforce on the layer which lead to the proppant having improved resistanceto crushing.

In contrast, lot B had the poorest resistance to crushing as evidencedby the highest weight percent crush (i.e. 12.6%). The proppants in lot Bwere made with a fine base material and coarse layer material. Duringthe final stage of the sintering process, the coarse layer materialcontinued to shrink after the fine base material has stopped shrinkingConsequently, the coarse layer was in tension which caused the layer tocrack. Evidence of the cracking can be seen in FIG. 10 which is ascanning electron micrograph at 180× magnification of a cross-section ofa proppant from lot B. The arrows point out the circumferential cracksthat extend around the perimeter of the proppant in the layer material.The photograph confirms that the base was not protected by a layer incompression which reduced the strength of the proppant. The fracturedlayer crumbled easily during the crush test which lead to the highweight percent crush test results.

Examples Lots E, F, G and H

Lots E, F, G and H were manufactured and crush tested to provide anotherillustration of how to improve the crush resistance of a proppant bycreating a compressive force on the proppant's layer material. The lotswere made from either a first bauxite material identified herein asmaterial M1, a second bauxite material identified herein as material M2,or a combination of M1 and M2. The M1 material had a two step sinteringcurve. With reference to the part numbers shown in FIG. 1, the firststep may be characterized as having point 26 equal to 1,033° C., point28 equal to 1,175° C., and point 32 equal to 1,117° C. The first step'sshrinkage was 2.0% and the thermal offset was 1150° C. The thermaloffset may be described as an intercept between tangents drawn throughpoint 32 and point 28. The second step of material M1 may becharacterized as having point 26 equal to 1,213° C., point 28 equal to1,560° C., and point 32 equal to 1,385° C. The second step's shrinkagewas 24% and the thermal offset was 1,493° C. The coefficient of thermalexpansion (CTE) of material M1 was 7.3×10⁻⁶/° C. The M2 material had asingle step sintering curve. With reference again to FIG. 1, the M2material's sintering step may be characterized as having point 26 equalto 1,162° C., point 28 greater than 1,560° C., and point 32 equal to1,443° C. The shrinkage was 25.3% and the thermal offset was 1,523° C.The CTE of material M2 was 8.9×10⁻⁶/° C. which was larger than thecoefficient of thermal expansion of material M1. In the final sinteringstage, the rate of linear contraction in M2 was higher than that in theM1 material. After forming and sintering all lots had a standard 20/40size distribution. Table 3 shows the combinations of base material andlayer material for the three lots.

TABLE 3 Base Material M1 M2 Layer M1 Lot E Lot F Material M2 Lot G Lot H

Lots E, F, G and H were manufactured as follows. The dry base materialand binder were placed into an Eirich mixer and mixed for 30 seconds.During the next 30 seconds water was added. As the mixer continued torotate, spheres of base material were formed. After approximately fourminutes of total mixing, a small amount of base material was added tothe damp spheres to dry the bases. The mixer was then stopped. For lotsF and G, the formed bases were removed and the mixer's pan and rotorwere cleaned. The cleaning step minimized the mixing of M1 and M2 whichcould have formed an undesirable intermediate mixture of the twomaterials on the surface of the base at the interface of the base andproppant. The formed bases in lots F and G were then separately returnedto the cleaned mixer for further processing. With regard to lots E andH, there was no need to remove the bases and clean the mixer becauseonly M1 material was used to make lot E and only M2 was used to make lotH. After the loading of each lot of bases, the mixer was restarted usingonly the pan motion. The rotor was not moving. Layer material was addedby sprinkling the same on top of the rotating bases. All lots were thensintered at 1450° C. The strength of each lot was then evaluated bydetermining the percent crush at 700 kg/cm². Shown in Table 4 are theresults of the crush testing.

TABLE 4 Base Material M1 M2 Layer M1 Lot E Lot F Material 9.3%  5.8% M2Lot G Lot H 7.2% 16.6%The data supports the conclusion that lot F had the lowest percentcrush. There are believed to be two reasons for lot F's low percentcrush. First, during the final stage of sintering, the rate of linearcontraction of the base material was higher than the layer material's.The difference between those two rates during the final stage ofsintering caused the layer to sinter in compression. The second reasonis due to the difference in the base material's coefficient of thermalexpansion and the layer material's coefficient of thermal expansion.Because lot F's base material was M2 which had a higher coefficient ofthermal expansion than the layer material, the base shrunk more than thelayer during the thermal cool down portion of the thermal cycle. Theresult was that the base exerted a compressive force on the layer whichimproved the proppant's ability to resist crushing.

In contrast, lot G was made with M1 as the base material and M2 as thelayer material. Lot G was weaker and had a higher weight percent crush.There are two reasons for lot G's low percent crush. First, during thefinal stage of sintering, the base material shrunk slower than the layermaterial due to the difference in shrinkage rates between the twomaterials. The difference in shrinkage rates during the final stage ofsintering caused the layer to sinter in tension and the base incompression. The compression upon the base enabled a greater degree ofdensification of the base than the layer. Second, the layer material(i.e. the M2 material) had a higher coefficient of thermal expansionthan the base material (i.e. the M1 material). The layer materialresponded to the cooling by shrinking more than the base. Consequently,the layer was in tension rather than compression while the base was incompression rather than tension which was in contrast to Lot F. Sinteredceramic materials that are in tension may fracture at lower pressurethan the same sintered ceramic materials that are in compression.Because of the extent of the sintering and thermal expansion differencesbetween the base and layer, the layer experiences tension forcessufficient for separation from the base such that Lot G had very littlelayer material on the M2 material and, thus, was essentially an M1material. The crush resistance of Lot G was better than Lot E becausethe base made from M1 experienced compression forces during sinteringwhich improved the densification of the base material. An earlierevaluation of a proppant made with M2 as the layer and M1 as the basebut without cleaning the mixer of M1 prior to using M2 showed a crushresistance of 24.4%. This much higher crush resistance occurred due tothe difference in processing steps. Not changing the mixer allowed aformation of intermediate layer between M1 and M2 material that improvedadhesion of M2 material to the surface of the M1 base. Despite thisimprovement in adhesion high tension forces present in n the M2 layerwere sufficient to weaken the proppant.

Proppants of this invention may be modified to improve their performancein certain down hole applications. For example, the proppants may bescreened to achieve a desirable particle size distribution as disclosedin U.S. Pat. No. 6,780,804 or coated with a polymeric material. Furthermodifications of the invention may occur to those skilled in the art andto those who make or use the invention. Therefore, it is understood thatthe embodiments shown in the drawings and described above are merely forillustrative purposes and are not intended to limit the scope of theinvention, which is defined by the following claims as interpretedaccording to the principles of patent law, including the Doctrine ofEquivalents.

1-14. (canceled)
 15. A process for manufacturing a ceramic element,comprising the steps of: (a) forming a spherically shaped non-sinteredbase of sinterable ceramic material; (b) depositing a non-sintered layerof sinterable material on the surface of the base thereby forming aspherically shaped non-sintered composite having a base coated with atleast one layer; and (c) exerting a compressive force on the ceramicelement by exposing the composite to a complete thermal cycle comprisinga thermal ramp up phase and a thermal cool down phase wherein during theramp up phase said base bonds to and shrinks more than said layer andafter said cool down phase said base exerts a compressive force on saidlayer.
 16. The process of claim 15 wherein during the exposure of thecomposite to the complete thermal cycle the layer material's rate oflinear change versus temperature accelerates and then decelerates, aftersaid deceleration has begun and prior to said cool down phase said basematerial's rate of linear change versus temperature exceeds said layermaterial's rate of linear change versus temperature.
 17. The process ofclaim 16 wherein said base material has a sintering profile that definesa nominal sintering temperature and said layer material has a sinteringprofile that defines a nominal sintering temperature at least 5° C. butno more than 250° C. less than said base material's nominal sinteringtemperature.
 18. The process of claim 17 wherein said layer material'snominal sintering temperature at least 20° C. but no more than 150° C.less than said base material's nominal sintering temperature.
 19. Theprocess of claim 15 wherein the step of forming a non-sintered basecomprises forming a spheroid.
 20. A process, for forming a ceramicelement, comprising the steps of: (a) forming a spherically shapednon-sintered base of sinterable ceramic material; (b) heating said baseto achieve at least partial sintering of the base; (c) depositing anon-sintered layer of sinterable material on the surface of the basethereby forming a spherically shaped composite having at least apartially sintered base coated with an non-sintered layer; and (d)exposing the composite to a complete thermal cycle that exceeds thesintering temperatures of the base and layer, wherein during saidthermal cycle the base and layer bond to one another and the basecontracts more than the layer thereby exerting a compressive force onthe layer.
 21. The process of claim 20 wherein said base material has amaximum theoretical density and, during step b, said base densifies toat least 25% of the base material's maximum theoretical density.
 22. Theprocess of claim 21 wherein said base densifies to less than 75% of thebase material's maximum theoretical densification.
 23. The process ofclaim 20 wherein the sintering temperature of the base in step b is atleast 25° C. less than the temperature at which the composite is heatedin step d. 24-33. (canceled)
 34. A process for manufacturing a ceramicelement, comprising the steps of: (a) forming a spherically shapednon-sintered base of sinterable ceramic material; (b) depositing anon-sintered layer of sinterable material on the surface of the basethereby forming a spherically shaped non-sintered composite having abase coated with at least one layer; and (c) exposing the composite to acomplete thermal cycle comprising at least a first thermal ramp up phaseand a final thermal cool down phase wherein after the initiation of saidfirst ramp up phase said base shrinks and said layer applies acompressive force to said base, and after the initiation of said finalcool down phase at least a portion of said layer separates from saidbase
 35. The process of claim 34 wherein said base has a known surfacearea and said layer covers no more than 75 percent of said surface area.36. The process of claim 34 wherein said base has a known surface areaand said layer covers no more than 50 percent of said surface area. 37.The process of claim 34 wherein said base has a known surface area andsaid layer covers no more than 25 percent of said surface area.
 38. Theprocess of claim 34 wherein said layer fractures prior to separatingfrom said base.
 39. The process of claim 34 wherein said base has acoefficient of thermal expansion and said layer has a coefficient ofthermal expansion greater than said base's coefficient of thermalexpansion.
 40. The process of claim 39 wherein the difference betweensaid base's coefficient of thermal expansion and said layer'scoefficient of thermal expansion is at least 40% but not more than 80%of said base's coefficient of thermal expansion.
 41. The process ofclaim 39 wherein after the initiation of said cool down phase said layerapplies an additional compressive force to said base.